Abstract:

Layered materials are provided that have surprisingly low thermal
conductivities. A plurality of layers of a selected material such as, for
example, tungsten diselenide, is formed by a modulated elemental
reactants method to produce a low thermal conductivity material. The
layers are generally stacked but substantially randomly arranged as
stacked.

Claims:

1. A composition, consisting essentially of a plurality of adjacent solid
layers and having a thermal conductivity of less than about 0.2 W
m-1 K.sup.-1.

2. The composition of claim 1, wherein the thermal conductivity is less
than about 0.05 W m-1 K.sup.-1.

4. The composition of claim 3, wherein the layers are substantially
randomly oriented about an axis perpendicular to a plane that is
substantially parallel to the layers.

5. The composition of claim 1, wherein the tungsten selenide is arranged
as a series of layers along an axis that is substantially perpendicular
to the layers, and the thermal conductivity is associated with heat
transfer in a direction parallel to the axis.

6. The composition of claim 1, wherein a thickness of the layers is
between about 1 nm and about 250 nm.

7. The composition of claim 6, wherein the thickness is between about 4 nm
and about 75 nm.

8. A method of fabricating a thermal material, comprising:depositing a
plurality of layers of a first constituent and a second
constituent;annealing the plurality of layers so as to produce
corresponding product layers wherein each product layer consists
essentially of a compound of the first constituent and the second
constituent.

9. The method of claim 8, wherein the plurality of product layers are
configured so as to be substantially randomly oriented about an axis
perpendicular to a plane that is substantially parallel to the layers.

10. The method of claim 9, further comprising annealing so that the layers
consist essentially of the crystalline compound.

11. The method of claim 9, wherein thicknesses of the product layers are
selected to be in a range of from about 1 nm to about 500 nm.

12. The method of claim 9, wherein the thicknesses of the product layers
are selected to be in a range of from about 5 nm to about 55 nm.

13. The method of claim 9, further comprising establishing a thermal
property by exposing the material to an ion beam flux.

14. The method of claim 9, wherein the first plurality of layers is
associated with a first thickness, and further comprising depositing a
second plurality of layers of the first and second constituent, wherein
the second plurality of layers is associated with a second thickness.

16. A composition, comprising:a first series of layers of a first
compound;a second series of layers of a second compound interleaved with
the layers of the first compound, wherein a thickness of the layers is
less than about 250 nm, and the layers are configured so as to be
substantially randomly oriented about an axis perpendicular to a plane
that is substantially parallel to the layers.

17. The composition of claim 16, wherein the first series of layers
consists essentially of Bi2Te3 and the second series of layers
consists essentially of TiTe.sub.2.

18. The composition of claim 17, wherein the first series of layers
consists essentially of CeSe and the second series of layers consists
essentially of NbSe.sub.2.

19. The composition of claim 17, wherein the first series of layers
consists essentially of BiSe and the second series of layers consists
essentially of NbSe.sub.2.

20. The composition of claim 16, wherein a total thickness of the first
and second series of layers is less than about 500 nm, and the layers of
at least one of the first series of layers and the second series of
layers are substantially randomly oriented layers.

Description:

CROSS REFERENCE TO RELATED APPLICATION

[0001]This application claims the benefit of U.S. Provisional Application
60/728,847, filed Oct. 20, 2006, and that is incorporated herein by
reference.

[0004]Thermoelectric devices can be configured to both create power and
pump heat, making such devices widely applicable in a variety of
commercial, consumer, and military applications. For example,
thermoelectrics have been suggested as power sources for remote sensors
that can extract power for their operation based on, for example,
existing thermal gradients such as a temperature difference between the
air and the sea. Thermoelectric devices have other desirable features for
many applications. For example, thermoelectric devices can operate with
no moving parts and thus can operate silently. These and other uses would
be significantly enhanced with higher performing thermoelectric devices.
While advances in thermoelectric technology have been made, improved
thermoelectric materials are necessary for many practical applications.

SUMMARY

[0005]Disordered materials are provided that exhibit surprisingly low
thermal conductivities, substantially lower than the thermal
conductivities of the corresponding bulk materials, and can permit
thermoelectric figures of merit (ZT) greater than about 2. Some
compositions consist essentially of tungsten selenide and having a
thermal conductivity of less than about 0.2 W m-1 K-1. In some
examples, the thermal conductivity is less than about 0.05 W m-1
K-1. In representative examples, compositions comprise a plurality
of tungsten selenide layers. In additional examples, the layers are
substantially randomly oriented about an axis perpendicular to a plane
that is substantially parallel to the layers. According to some examples,
the tungsten selenide is arranged as a series of layers along an axis
that is substantially perpendicular to the layers, and the thermal
conductivity is associated with heat transfer in a direction parallel to
the axis. In representative examples, a thickness of the layers is
between about 1 nm and about 250 nm or between about 4 nm and about 75
nm.

[0006]Methods of fabricating a thermal material comprise depositing a
plurality of layers of a first constituent and a second constituent and
annealing the pluralities of layers so as to produce a corresponding
plurality of product layers, wherein each product layer consists
essentially of a compound of the first constituent and the second
constituent. In some examples, the product layers are configured so as to
be substantially randomly oriented about an axis perpendicular to a plane
that is substantially parallel to the product layers. In additional
examples, the constituent layers are annealed so that the product layers
consist essentially of the crystalline compound. In further examples,
thicknesses of the constituent layers are selected to be in a range of
from about 1 nm to about 500 nm. According to further examples, the
thicknesses of the constituent layers are selected to be in a range of
from about 5 nm to about 55 nm. In some examples, a thermal property is
established by exposing the material to an ion beam flux. In additional
representative examples, the first plurality of layers is associated with
a first thickness, and a second plurality of layers of the first and
second constituents is deposited, wherein the second plurality of layers
is associated with a second thickness. In one example, the product layers
consist essentially of tungsten selenide. In other examples, the second
plurality of layers is associated with one or more additional
constituents.

[0007]Compositions comprise a first series of layers of a first compound
and a second series of layers of a second compound interleaved with the
layers of the first compound. A thickness of the layers is less than
about 250 nm, and the layers are configured so as to be substantially
randomly oriented about an axis perpendicular to a plane that is
substantially parallel to the layers. In some examples, the first series
of layers consists essentially of Bi2Te3 and the second series
of layers consists essentially of TiTe2. In additional examples, the
first series of layers consists essentially of CeSe and the second series
of layers consists essentially of NbSe2. In further representative
examples, the first series of layers consists essentially of BiSe and the
second series of layers consists essentially of NbSe2. In still
additional embodiments, a total thickness of the first and second series
of layers is less than about 500 nm, and the layers of at least one of
the first series of layers and the second series of layers are
substantially randomly oriented layers.

[0008]The foregoing and other objects, features, and advantages of the
disclosed technology will become more apparent from the following
detailed description, which proceeds with reference to the accompanying
figures.

BRIEF DESCRIPTION OF THE DRAWINGS

[0009]FIG. 1 is a graph of in-plane diffraction data obtained with an 18.5
keV energy beam in which all (hk0) diffraction peaks of tungsten
diselenide can be identified.

[0010]FIG. 2 contains graphs of measured thermal conductivities of
WSe2 layers as a function of measurement temperature. Each curve is
labeled with a layer thickness and data for a bulk specimen is included
for reference. The ion-irradiated sample was subjected to a 1 MeV
Kr.sup.+ ion dose of 3×1015 cm-2. The solid line marked
Λmin is a calculated minimum thermal conductivity for
WSe2 based on a longitudinal speed of sound measured in a
cross-plane direction (1.6 nm/ps) and an estimate of a transverse speed
of sound (1.15 nm/ps).

[0011]FIG. 3 is a graph of thermal conductivity as a function of
irradiation dose for WSe2 films having a 2 nm thickness. Irradiation
was based on 1 MeV Kr.sup.+ ions.

[0012]FIG. 4 illustrates atomic positions in a model layered WSe2
structure corresponding to a stacking disorder. Approximate positions of
a heat sink and a heat source separated by 8 mm are indicated.

[0013]FIG. 5 is a graph of a steady state temperature profile obtained
with a non-equilibrium, heat source-sink method. The solid line depicts a
linear fit to a central region between a heat source and a heat sink. The
dashed line is an similar fit but for a structure with a heat source/heat
sink separation of 16 mm.

[0015]FIG. 7 is a graph of thermal conductivity as a function of annealing
temperature for WSe2 films with nominal thicknesses of 70 nm (full
circles) and 360 nm (open circles). Annealing was done in nitrogen
atmosphere for one hour at each temperature. Data for MoSe2 films
with nominal thickness 70 nm (full triangles) is included for comparison.

[0016]FIG. 8 is a graph of thermal conductivity of a Si substrate as a
function of irradiation dose. Samples were irradiated with 1 MeV Kr.sup.+
ions and doses from 1×1013 cm-2 to 1×1016
cm-2.

DETAILED DESCRIPTION

[0017]Turbostratically disordered materials are disclosed that provide
surprisingly low thermal conductivities and can serve to control heat
flow as well as serve as thermoelectric materials. Such materials can be
formed as so-called "superlattices" that are laminates of two or more
different compounds. Individual components of such a superlattice can be
prepared in the same manner as the superlattice (vapor deposition and
annealing of, for instance, WSe2), but the superlattice can exhibit
a thermal conductivity that is substantially lower than that expected for
the bulk material. Repeated layers of a single material can also be used,
and superlattice arrangements are not required.

[0018]Turbostratically disordered materials as described herein are
neither completely crystalline nor completely amorphous. Such materials
generally are ordered in a series of planes and along an axis
perpendicular to the planes, but the planes are randomly or
quasi-randomly stacked so there is no or reduced ordering between the
planes. If materials with suitable electronic properties such as, for
example, thermoelectric properties are formed with turbostratic disorder,
then thermal conductivity can be lowered, thereby improving
thermoelectric properties. Such turbostratically disordered materials can
also be used generally in applications in which relatively low thermal
conductivity is desired. Thus, "turbostratically disordered" structure
permits superior thermal and thermoelectric properties.

[0019]Low thermal conductivity solids are provided by arranging a series
of layers of one or more constituents (elements or compounds) adjacent
each other. The layers typically have long range order such as the
crystallographic order associated with bulk constituents. However, the
layers are randomly stacked or otherwise arranged so that there is little
long range order among the layers. For example, a composition can be
formed as a series of substantially identical crystalline layers similar
to thin plates. Each plate can be oriented so that a selected crystal
axis (for example, a z-axis) is substantially perpendicular to the plate,
while other crystal axes are in a plane of the plate or otherwise
arranged. The plates are stacked so that each plate shares a common
z-axis direction but so that one or more crystal axes are randomly
arranged. As used herein, a random arrangement is a configuration in
which the ordered arrangement of a plate within a plane perpendicular to
a stacking direction (a z-axis direction) plates is substantially
uncorrelated to the ordered arrangement within other plates. Thus, an
ordered arrangement with an xy plane of a particular plate is
uncorrelated or weakly correlated to the ordered arrangement in xy-planes
of other plate. In some examples, adjacent or close layers can exhibit
some correlation in their ordering, but this correlation can be weak and
tends to diminish as a function of layer separation. In other examples,
layers are stacked along a z-axis direction, but the layers have
arbitrary internal ordering. It will be appreciated that layers need not
have long range order throughout, and layers can have varying
orientations as a function of position. For convenience, such
arrangements are referred to herein as disordered.

[0020]Typically compositions consist of a plurality of such layers that
are formed by deposition of a series of layers and layer constituents on
a substrate. Subsequent processing is carried out to provide order within
the layer, but so that the layers do not adopt a common, coherent order.
The disclosed compositions are solid compositions having densities
comparable to the bulk densities of the layer materials. Typically, layer
and multilayer densities are at least about 50% of bulk density.

[0021]Representative turbostratically disordered materials described
herein are based on WSe2 and BiTe/SbTe alloys and other
compositions. For example, superlattice compounds consisting of
interleaved layers of bismuth telluride and/or antimony telluride with
structurally related van der Waal compounds are disclosed.

[0022]For superior thermoelectric performance, a product of the electrical
conductivity and the Seebeck coefficient squared (the so-called power
factor) of a material should be relatively large and the thermal
conductivity relatively low. Disclosed herein are representative examples
of materials having surprisingly low thermal conductivities as well as
unexpected electrical properties. For example,
(Bi2Te3)x(TiTe2)y compounds are semiconducting
for small values of y, even though TiTe2 is reported to be a
semimetal.

[0023]Films of selected superlattice compositions can be formed using, for
example, a modulated elemental reactant method such as described in, for
example, PCT Patent Publ. 2004/012263 and U.S. Pat. No. 5,994,639. In
general, thermodynamically metastable crystalline compounds having a
selected crystal structure are prepared through controlled
crystallization of amorphous reaction intermediates formed by
low-temperature interdiffusion of modulated elemental reactants. The
modulated elemental reactants are generally produced by layering thin
films of the elements, wherein the layers are thin enough that they will
interdiffuse at low temperatures, forming an amorphous reaction
intermediate, before they nucleate (i.e., crystallize). The amorphous
reaction intermediate for each system typically nucleates exothermically
at about 200° C., forming a selected compound. At temperatures
above about 500° C., such metastable compounds tend to decompose
exothermically forming a thermodynamically stable mixture of binary
compounds and elemental components.

[0024]Some disclosed compounds comprise crystalline alloys of two or more
solid-state reactants and are produced on a surface of a solid substrate,
such as a silicon wafer. Each crystalline alloy is formed by first
forming one or more modulated elemental reactants or "repeat units," of
reactant layers superposedly on the substrate surface. Each repeat unit
may contain the same number of elemental layers. The stoichiometry of the
desired crystalline alloy is determined by the relative thicknesses of
the elemental reactant layers comprising the repeat units. When at least
three reactants are used, the stoichiometry is determined in part by the
number of layers of a particular reactant in a repeat unit relative to
the number of layers of each of the other reactants in the repeat unit.

[0025]Modulated elemental reactants are typically prepared using an
ultra-high-vacuum deposition apparatus. The repeat units are prepared on
substrate wafers comprised of materials such as (but not limited to),
silicon, quartz, or float glass. A group of such wafers is typically
mounted in the vacuum chamber of the deposition apparatus on sample
mounts to undergo planetary rotation in a vacuum chamber during
deposition. Reactant layers can be deposited on the wafers using any of
various methods known in the art including, but not limited to,
sputtering, vapor deposition, and electron-beam gun deposition.
Deposition rates typically are adjusted within a range of about 0.05-0.2
nm/sec. Deposition rates may, however, be much higher or lower depending
on variables known to those skilled in the art. The vacuum in the chamber
during deposition is typically between 10-7 and about 10-9
Torr.

[0026]Layers, when deposited, can be either amorphous or crystalline (as
can be determined via x-ray diffraction). Interdiffusion of either type
of layer can be conducted at a temperature that will overcome the
activation energy of diffusion for the various layers. In general, the
activation energy of diffusion for crystalline reactants is higher than
for amorphous reactants. After forming a repeat unit of the reactants on
the substrate, the repeat units are heated to an interdiffusion
temperature for the reactants. The interdiffusion temperature is less
than the nucleation temperature for the reactants. A suitable
interdiffusion temperature, generally in the range of several hundred
degrees Celsius, can be readily determined by performing differential
scanning calorimetry (DSC) of the modulated composite using methods
generally known in the art. The interdiffusion temperature is maintained
until the reactants have achieved a homogeneous interdiffusion, thereby
forming a homogeneous amorphous alloy of the reactants.

[0027]After forming the amorphous alloy, the amorphous alloy is heated to
a nucleation temperature. The nucleation temperature is maintained until
the amorphous alloy becomes fully crystallized. With certain alloys,
however, once nucleation begins, crystallization progresses to completion
even when the temperature of the alloy is reduced to below the nucleation
temperature before crystallization is complete. In some examples,
nucleation and interdiffusion are produced at a single "annealing"
temperature.

[0028]For any modulated composite, there is typically a preferred
thickness parameter associated with a maximum repeat-unit thickness than
can interfuse to homogeneity without triggering nucleation. In general,
keeping the repeat-unit thickness to about 10 nm or less effectively
allows formation of a homogeneous amorphous alloy of reactants without
nucleation, but thicknesses of up to 500 nm or larger can be used for
some materials.

[0029]Materials that comprise interleaved Van der Waal compounds can
provide several advantages such as, for example, superior doping density
control, reduced electron scattering, turbostratic disorder due to
lattice mismatches, strain relief (including thermal strain relief) as
layers are free to "slide over" one another. A large number of van der
Waal (VDW) compounds with a wide variety of physical properties can be
suitable, including high density of states metals (VX2, NbX2,
TaX2 wherein X is a chalcogen), semiconductors of varying band gaps
(MoX2, WX2, Ga2X3, Sb2X3, and
Bi2X3 where X is a chalcogen, semimetals (TiX2, ZrX2,
and HfX2), and magnetic materials (transition metal intercalates of
dichalcogenides).

[0030]A representative method of preparing a superlattice system of a
selected composition includes calibrating deposition sources so that a
stoichiometrically appropriate composition of elements for each component
of the desired final superlattice can be deposited. This calibration can
be done by, for example, making six multilayer samples, three containing
a repeating unit with a fixed thickness of a first constituent A and
varying thickness of a second constituent B, and three samples with a
fixed thickness of B and varying thickness of A. Low angle x-ray
diffraction of the samples can be used to determine repeat layer
thicknesses based on a position of the Bragg reflections resulting from
the layering. Plotting the measured thickness of each set of three
samples against the intended thickness of the varying layer produces the
thicknesses of the component layers that can be used to establish a
tooling factor. Electron microprobe data collected as a function of
accelerating voltage can be fit to yield the composition of these
samples. This information is used to create a series of three samples
with compositions matching the stoichiometry of the desired component
compound, varying the intended total thickness of the repeating unit.
These samples are then annealed at low temperatures (typically less than
about 500° C.) to yield the desired crystalline compound to obtain
both processing information and an amount the films contract on
crystallization. The repeat layer thickness required to avoid interfacial
nucleation of competing compounds is determined. Preparing samples with
the bilayer thicknesses below this value permits the desired compound to
be formed directly from the amorphous precursor. With all of this
information, it is straightforward to calculate the bilayer thicknesses
required to form a single unit cell of the desired compound.

[0031]Having obtained this information for the desired component
compounds, the individual bilayer units calculated to give a single unit
cell can be repeated to give the desired number of unit cells of each
component and interleaved to produce a reactant that will evolve to the
desired compound. In some examples, unit cells of a single type or
multiple types are used. Typically, diffraction data collected as a
function of annealing temperature and time can be used to select
preferred annealing conditions based small angle and large angle
diffraction peaks. Rapid thermal annealing and/or extended low
temperature annealing is used to optimize grain growth while limiting
interdiffusion of the layers. Suitable materials can include
(Bi2Te3)x(TiTe2)y,
(Bi2Te3)x(HfTe2)y,
(Sb2Te3)x(TiTe2)y, and
(Sb2Te3)x(HfTe2)y based on a 5 layer VDW
compound (Te--Bi--Te--Bi--Te) and a 3-layer VDW compound (Te--Hf--Te),
(Bi2Te3)x(TiTe2)y(Sb2Te3)z based
on two 5-layer VDW compounds interleaved with a 3-layer VDW compound,
(Bi2Te3)x(PbTe)y based on a 5 layer VDW compound
interleaved with a rock salt structure, and
(TiTe2)x(PbTe)y based on a 3 layer VDW compound
interleaved with a rock salt structure. Doping of the rock salt layer
with electron donors (3+ cations in place of lead) or electron deficient
(1+ cations in place of lead) can be used to select suitable charge
transfer characteristics.

[0032]Initial synthesis optimization and electrical characterization can
be done on thin film samples. Typically 200-400 nm thick films based on
multiple repeat units are prepared on either glass or sapphire substrates
for electrical measurements, on smooth silicon wafers for process
optimization and on mis-cut quartz for structural characterization. Films
can be analyzed with a sequence of low and high angle x-ray diffraction
(XRD) measurements, SEM, Microprobe and TEM to characterize their
structure. The initial electrical measurements on a system are collected
as a function of annealing temperature and time because there are
typically large changes in both conductivity and Seebeck coefficients
during annealing, probably due to non-equilibrium defect concentrations
trapped in these materials during crystallization. This procedure is
useful as extended annealing allows measurement of properties as a
function of carrier concentration with only a single sample. This
procedure is used to select doping and annealing conditions to obtain
predetermined electrical properties.

REPRESENTATIVE EXAMPLES

[0033]Methods and apparatus are described for particular examples
pertaining to compounds based on two or three different component
constituents with a controlled repeat pattern. For example, different
repeat patterns of compositions such as ABC, ABCB etc., wherein A, B and
C represent different constituent compounds can be provided and
controlled. (Bi2Te3)x(TiTe2)y, WSe2, and
WSe2/W superlattices and films having extremely low thermal
conductivities can be produced. Bulk superlattice pellets such as a
2×2×8 mm3 (Bi2Te3)5(TiTe2)4
superlattice pellet with a c-lattice orientation perpendicular to a
pellet long axis can be formed. Representative examples such as a 500 nm
film of (Bi2Te3)5(TiTe2)4, and various
compositions of the form (Bi2Te3)x(TiTe2)y have
been prepared. Modulation of layering decreases as a function of
increasing annealing temperature, but such films still demonstrate
layering structure and can exhibit lowered thermal conductivity. In other
examples, several films of materials of the form
(Bi2Te3)x(TiTe2)y(Sb2Te3)z and
(Bi2Te3)x(TiTe2)y(Sb2Te3)z(TiTe2)-
y have been demonstrated. Other superlattices such as, for example,
(CeSe)x(NbSe2)y and (BiSe)x(NbSe2)y have
been prepared.

[0034]Multilayer thin films of metals and metal oxides can be configured
to have surprisingly low thermal conductivity. Typically, multilayer
compositions having layer thicknesses and spacings of less than about 50
nm, 25 nm, 10 nm, or 5 nm can have a thermal conductivity substantially
less that that of a corresponding homogenous metal or metal oxide. Low
thermal conductivity of such multilayer compositions may be due to
thermal resistance at layer interfaces.

[0035]In an example, ten n-type (Bi2Te3)6(TiTe2)3
superlattice film samples were produced having similar low angle and high
angle diffraction patterns. After annealing, all films were
crystallographically similar based measured diffraction patterns. Average
resistivity was about 0.8 mOhm-cm at room temperature with a range of
about 0.5 to 1.0 mOhm-cm. All of the films had similar temperature
dependences, with different low temperature intercepts, suggesting that
the differences in the films resulted from a difference in the
concentration of defects. The measured Seebeck coefficients at room
temperature ranged from -30 to -100 μV/K with an average value of -50
μV/K. The Seebeck coefficient of these films increases with annealing
time, increasing to about -140 μV/K, suggesting that the number of
carriers is being reduced with annealing. About 1.6 grams of a
(Bi2Te3)6(TiTe2)3 superlattice was formed by
depositing approximately 20 thick films of this material on polymer
coated six inch wafers.

[0036]In another representative example, a thermal conductivity of a
disordered thin film of a layered crystal of tungsten diselenide
(WSe2), can be less than about 0.2 W m-1 K-1 and at least
as small as about 0.05 W m-1 K-1. A minimum thermal
conductivity for a bulk specimen of this material is about 0.3 W m-1
K.-1 In some examples, disruption of a layered structure by ion
irradiation can produce a substantial increase in thermal conductivity.
Thus, ultra-low thermal conductivity in this material may be of function
of material order, and the low thermal conductivities can be produced by
random stacking of well-ordered WSe2 crystalline sheets.

[0037]WSe2 thin films are synthesized by a modulated elemental
reactants (MER) method such as described in Moss et al., Chemistry of
Materials 8:1625 (1996). MoSe2 or other films can be similarly
synthesized. Sequential bilayers of W (or Mo) and Se are deposited in an
ultra high vacuum (about 10-7 Torr) onto unheated Si (100) wafers
with a stoichiometry of 1:2. The samples are subsequently annealed for
one hour at elevated temperatures in N2 atmosphere to promote the
formation of the desired layered structures. In the WSe2 structure,
a hexagonal sheet of W atoms is bound to two Se layers by strong
covalent-ionic bonds and each WSe2 layer is bonded to adjacent
layers by weak van der Waals forces. A single crystal foil of WSe2
was used to provide a comparison between the thermal conductivities of a
well-ordered crystal and the disordered thin films. Thermal conductivity
was measured using time-domain thermoreflectance as described in, for
example, C. A. Paddock, G. L. Eesley, J. Appl. Phys. 60: 285 (1986) and
R. J. Stoner, H. J. Maris, Phys. Rev. B 48: 16373 (1993) using a thin
layer of Al (60-85 nm thick) deposited by magnetron sputtering as a
transducer layer. The details of the data acquisition and analysis have
been described previously in, for example, D. G. Cahill, Rev. Sci.
Instrum. 75:5119 (2004). Thermal conductivity can be determined by
comparing the time dependence of the ratio of in-phase Vin and the
out-of-phase Vout signals from a lock-in amplifier to calculations
based on a thermal model.

[0038]As shown in FIG. 1, diffraction data for a representative sample
film shows all expected (hk0) diffraction maxima and can be used to
determine a value of a lattice parameter a that corresponds to the known
value. The intensities of the (hk0) maxima remain constant with sample
rotation indicating a random rotational distribution of the sheets. Only
weak and very broad (hk1) diffraction maxima are observed on searching
reciprocal space, suggesting a limited amount of rotational order between
WSe2 layers and a limited domain size.

[0039]FIG. 2 shows measured thermal conductivity of annealed films,
conductivity of single crystal WSe2, and a predicted minimum thermal
conductivity Λmin. The theoretical minimum thermal
conductivity is based on the assumption that the lifetime of every
vibrational mode in a Debye model of the solid has a lifetime of one-half
of the vibrational period; the inputs to this phenomenological model are
the number density of atoms and the speeds of sound. The longitudinal
speed of sound in the cross-plane direction of nominal 360 nm thick films
is vL=1.6 nm ps-1 using picosecond acoustics. With vL=1.6
nm ps-1 and a mass density of p=9.2 g cm-3, the elastic
constant is C33=23.6 GPa, comparable to C33 for NbSe2 and
TaSe2. The transverse speed of sound vT can be estimated as
vT=1.15 nm ps-1 from vL and a ratio of C33 to
C44 previously measured for NbSe2 and TaSe2.

[0040]The lowest thermal conductivity of WSe2 films measured at 300 K
is 0.048 W m-1 K-1 for a 62 nm thick layer, 30 times smaller
than the cross-plane thermal conductivity of single-crystal sample of
WSe2 (FIG. 2) and a factor of 6 smaller than the predicted minimum
thermal conductivity. The conductivity of the 62 nm thick film is smaller
than the conductivity of a thinner film (24 nm thick) or a thicker film
(343 nm thick). Thermal conductivity of single crystal WSe2 is
approximately proportional to the reciprocal of the absolute temperature
as expected for a dielectric or semiconductor material where heat
transport is dominated by phonons with mean-free-paths limited by
anharmonicity.

[0041]The data of FIGS. 1-2 suggest that very low thermal conductivities
are produced by random-stacking of well-crystallized WSe2 sheets. To
test this idea, specimens were subjected to irradiation by energetic
heavy ions to disrupt the crystalline order in the thin film samples.
Thermal conductivity as a function of irradiation dose is shown in FIG.
3. Because TDTR requires knowledge of the thermal conductivity of the
substrate, bare silicon substrates were irradiated with the same range of
ion fluences, and the thermal conductivity of the ion-irradiated Si was
also measured as shown in FIG. 8. Simulations predict that 1 MeV Kr.sup.+
ions are transmitted by 24 nm thick WeSe2 films and penetrate into a
Si substrate to a range of ˜700 nm. The effect of the ion
bombardment is most visible at highest dose (3×1015 ions
cm-2) and at that dose thermal conductivity is increased by about a
factor of 5. Apparently, ion-induced damage to the stacking of WSe2
sheets introduces disorder that reduces localization of vibrational
energy and enhances the transfer of vibrational energy between adjacent
sheets.

[0042]For further understanding of these films, models based on 6-12
Lennard-Jones (LJ) potentials of the form

U ( r ) = 4 [ ( σ r ) 12 - ( σ r )
6 ]

were developed, wherein .di-elect cons. is the energy scale and σ is
the length scale. Two sets of .di-elect cons. and σ parameters are
used: for interactions within a single layer, .di-elect cons.=0.91 eV and
σ=2.31 Å, and for the interaction between layers, .di-elect
cons.=0.08 eV and σ=3.4 Å. This selection is used to achieve a
reasonable fit the WSe2 crystal structure and C11 (200 GPa) and
C33 (50 GPa) elastic constants. For computation efficiency a cutoff
of 5.4 Å is used, both potentials with both energy and forces shifted
such that they are zero at the cutoff. The cross sectional area of the
simulation cell is 15.3×13.3 Å. Along the (0001) direction two
sizes were selected, 160 and 320 Å. Periodic boundary conditions were
used for all directions. Newton's equations of motions were solved by the
5th order predictor corrector algorithm with a time step
Δt=1.8×10-15 s.

[0043]The simulation setup for the thermal transport measurement is
depicted in FIG. 4. First, the structure is equilibrated at T=300 K and
zero pressure for 100,000 time steps. In the next step, the global
thermostat is turned off, however, thermal energy is supplied to a
WSe2 layer and removed from a layer at a distance equal to the half
of the cell size along the (0001) direction, labeled as the z direction.
Atomic velocities were scaled up (down) in the heat source (respectively
heat sink) regions such that heat was added at a constant rate of
dQ/dt=10-6 eV/time step to the source and removed at the same rate
from the sink. The temperature profile along the z-direction was
monitored by calculating total kinetic energy of atoms in each WSe2
layer and performing time averages. Due to the small energy barrier for
shearing of the WSe2 structure and the small cross sectional area of
the simulation cell these structures exhibited thermally exited local
shearing events leading to disorder in layer stacking (FIG. 4).

[0044]After a transient time of 5 to 20 million steps depending on the
system size, a steady state temperature profile is established as shown
in FIG. 5. The thermal conductivity Λ is obtained using Fourier's
law. The temperature vs. position slopes and thus the thermal
conductivities of 16 nm and 32 nm long structures are essentially the
same within the statistical error, Λ=0.03-0.06 W m-1
K-1.

[0045]While the thermal conductivity of disordered, layered crystals is
significantly less than the predicted minimum thermal conductivity for
the cross-plane direction, the thermal conductivity of ion irradiated
WSe2 can be comparable to the predicted minimum thermal
conductivity. These results suggest that control of both order and
disorder in the disordered stacking of well-ordered crystalline sheets of
a layered crystal can produce unexpected and dramatic reductions in the
thermal conductivity. The WSe2 films described in this example are
poor electrical conductors in the cross-plane direction. Semiconductors
with similar structural features and good electrical mobility can be
fabricated into disordered, layered crystals to form superior
thermoelectric materials.

[0046]Tungsten selenide layer fabrication is described more fully as
follows. Sequential bilayers of W and Se are deposited in an ultra high
vacuum chamber (10-7 Torr background pressure) onto unheated Si
(100) wafers with a stoichiometry of 1:2. Subsequent annealing is
performed in an N2 atmosphere to promote the formation of the
desired layered structures. Films with nominal thickness of 30, 70 and
350 nm are formed. The as-deposited wafer with 30 nm WSe2 nominal
thickness is annealed at 625 C for 1 hour. The as-deposited wafer with 70
nm WSe2 nominal thickness is divided and individual samples are
annealed for 1 hour at temperatures of 200, 350, 500 and 650° C.,
respectively. The as-deposited wafer with 350 nm WSe2 nominal
thickness is also divided and individual samples are annealed for 1 hour
at temperatures of 200, 625 and 650° C., respectively. An
as-deposited sample of each wafer is used as control sample.

[0047]Films are characterized by x-ray diffraction (XRD), electron probe
microanalysis (EPMA), and by Rutherford backscattering spectrometry
(RBS). Film stoichiometry is measured using a Cameca SX-50 Electron Micro
Probe Analyzer (20 nA current and 1 μm spot size) collecting data at
multiple spots at 8, 12 and 16 kV beam energies. EPMA provides a reliable
quantitative measure of film composition provided careful attention is
paid to eliminating substrate interference and to the variation of
excitation volume with incident-beam energy. Data is refined using
STRATAGEM software, a thin-film composition software program that
accounts for sample geometry and substrate. Total layer thickness is
derived from the areal densities of W and Se measured by Rutherford
backscattering spectrometry (RBS) with 2 MeV He.sup.+ ions. Data from RBS
measurements is analyzed using the SIMNRA software. The layered structure
of the samples was studied using X-ray diffraction scans of the
as-deposited and annealed samples collected on a Brucker X-Pert thin film
diffractometer or at the APS UNICAT beamline. Data from X-ray scans was
refined via Rietveld analysis.

[0048]Structure analysis of the samples by x-ray diffraction (XRD) shows
that the films have a layered structure with as deposited samples
exhibiting weak broad (001) diffraction maxima. Peak intensity and
sharpness increases as a function of annealing temperature. Crystal size
calculations base on the Scherrer equation yields values of 5 nm, 10 nm
and 53 nm for samples with 8 (5.32 nm), 16 (10.59 nm) and 80 (52.96 nm)
Se--W--Se layers respectively, implying that the entire thickness of the
films have crystallized. The presence of only the (002), (006) and (008)
peaks of WSe2 suggests that the WSe2 formed is
crystallographically aligned with the substrate. The WSe2 sheet
thicknesses calculated from the (001) Bragg peaks parameters are 0.66 nm,
larger than the 0.649 nm reported in the literature for 2H-WSe2.
Rietveld analysis of the structure along the c-axis suggests that this
thickness increase results from a small amount of W (˜3%)
intercalated between the WSe2 layers.

[0049]Thermal conductivity was measured using time-domain
thermoreflectance using a 60-85 nm thick Al layer deposited by magnetron
sputtering as a transducer layer. Because of the very low thermal
diffusivity of the WSe2 films, data was acquired at a low modulation
of frequency for the pump beam of 580 kHz in addition to data acquired at
the modulation frequency of 10 MHz that is more typical in such
measurements. The pump and probe beam optical beams are focused on the
surface of the samples using a microscope objective lens of 40 mm or 20
mm focal length, producing a 1/e2 radius of the focused spot of 12.6
or 6.3 μm, respectively. Typical laser power incident at the surface
of the sample is about 3 mW for both the pump and probe beams. The
steady-state temperature rise at the surface of the thin film samples is
typically ˜3 K, highest temperature rise being 7 K for a 343 nm
layer at 88 K. Highest steady state temperature rise at the surface of
the single crystal sample is 20 K at 300 K. Corrections for the sample
temperature are considered in the thermal model to take into account the
steady-state heating. Samples can be mounted in a LN2 cryostat for
measurements in a range of 90-300 K.

[0050]The thermal conductivity is determined by comparing the time
dependence of ratio of the in-phase Vin and the out-of-phase
Vout signals from a lock-in amplifier to calculations using a
thermal model. The thermal model has several parameters (pump modulation
frequency, laser spot size, and the thickness, thermal conductivity and
heat capacity of each layer) but the thermal conductivity of the sample
film or bulk crystal is the only important unknown. The aluminum layer
thickness is derived from the areal density of Al measured by Rutherford
backscattering spectrometry (RBS). Aluminum thermal conductivity is
calculated using the Wiedemann-Franz law from 4 point probe measurements
of the electrical resistivity at room temperature. Thermal conductivity
of Al at lower temperatures is estimated from the values at 300 K
assuming a constant residual resistivity. Heat capacity of Al and Si and
the thermal conductivity of the Si are taken from the literature.
Literature values for heat capacity of WSe2 measured at 300K are
1.94 and 1.95 J cm-3 K-1, respectively. This value is 3%
smaller than the value estimated from classical limit of 3 kB per atom
(2.01 J cm-3 K-1). The thermal conductance of the Al/sample
interface is also adjusted in the model to fit the data but because of
the low thermal conductivities of the materials considered here, this
interface conductance has very little influence on the measurement of the
thermal conductivity.

[0051]The accuracy of the thermal conductivity measurement can be
estimated by calculating the square-root of the sum of the squares of
uncertainties propagated from measurements of the thickness and thermal
conductivity of the aluminum layer, thickness of the MoSe2 or
WSe2 film, the pump and probe beam spot radius diameters. The
uncertainties propagated for each parameter are estimated by multiplying
the experimental errors by the ratio of the sensitivity to the respective
parameter and the sensitivity to the thermal conductivity of the
transition metal diselenide film. The sensitivity is defined as:

S α = ln ( - V i n V out ) ln
α ,

wherein α is any parameter of the thermal model

[0052]FIG. 6 shows the variation of the sensitivity factors for different
parameters as a function of WSe2 layer thickness. The sensitivity to
thermal properties of the Al and the WSe2 layer is important when
the thermal penetration depth l in WSe2 is larger then the thickness
of the layer; l=(D/w)1/2≈100 nm, where D≈0.0003
cm2 s-1 is the thermal diffusivity of the WSe2 layer and
w=3.6×106 s-1 is the angular frequency of the modulation
of the pump beam. As the thickness of the WSe2 layer increases
(h.sub.WSe2>100 nm), the sensitivity factor for thermal conductivity
of WSe2 drops. For thicker samples, the spot size w0 also
becomes more important.

[0053]The uncertainties in measuring the thickness of aluminum layer, the
thickness of the WSe2 layer and the laser spot size are estimated at
2% each. The uncertainty for the thermal conductivity of the Al layer is
estimated at 3% at 300 K and 15% at 80 K due to accuracy of the
deviations from the Wiedemann-Franz law. Overall errors are shown as
error bars in FIG. 2 and range between 5% at 300 K and 15% at 80 K.

[0054]Irradiation with 1 MeV Kr.sup.+ ions is used to disrupt the
crystalline order in the WSe2 films. The fluences used are in the
range of 1×1012 to 3×1015 cm-2. Bare silicon
substrates were irradiated with the same range of ion fluences and the
thermal conductivity of the ion-irradiated Si (FIG. 8) was used as a
parameter in the TDTR analysis of the WSe2 films. A low current (30
nA) minimized the amount of self annealing in the samples. The Ion
Stopping and Range in Targets module in SRIM 2003 software package is
used to predict the location and extent of the buried amorphous Si layer
formed in the substrates as a result of the irradiation.

[0055]Bulk materials can also be produced. For example, sequential 0.4
μm films can be prepared on six inch Si substrates coated with PMMA.
Multiple films are prepared and structurally characterized to obtain
enough material for the bulk samples. This thickness can be limited by
the stability of the evaporation sources and quartz crystal monitors used
in a deposition system. Placing these wafers in acetone dissolves the
PMMA and the resulting superlattice flakes are collected via filtration.
This is repeated to obtain 0.5 grams required to press a bulk pellet.
Since the flakes have high aspect ratios, they stack like cards when
loaded in to the hot press cell, resulting in a crystallographically
aligned pressed pellet. Pellets are analyzed with a sequence of low and
high angle XRD measurements, SEM, Microprobe and TEM.

[0056]The above methods can be applied to produce many other material
combinations that have various layer thicknesses and total thicknesses.
In addition, bulk samples can be provided. In view of the many possible
embodiments to which these principles may be applied, it should be
recognized that the illustrated embodiments are only preferred examples
and should not be taken as limiting. Rather, the scope of the invention
is defined by the following claims. We therefore claim as our invention
all that comes within the scope and spirit of these claims.